KILLEEN, Texas—U.S. Army Maj. Nidal Hasan, who admitted during his court-martial that he went on a shooting rampage at Fort Hood in 2009 because he believed the military was at war with Islam, was sentenced to death on Wednesday by a jury of fellow officers.

Maj. Hasan, a U.S.-born Muslim who worked at the Texas Army base as a psychiatrist, showed no response as the head of the jury rendered the unanimous sentence Wednesday...